Who is the person you should talk to at the Nursing Home for issues like baths and clean rooms and bathrooms? Is it the Social Worker?

I guess it depends on how large the facility is. At Moms each floor had a Nursing supervisor who was in charge of her care plan. The aids and LPNs on the floor all reported to her. She was the one I would go to with concerns like yours and she had the authority to fix those issues. Bypassing her and going directly to the DON in that facility would be jumping over her head and would have hurt our relationship. Even the Admin on Moms floor had the authority to fix minor issues like those. So I would suggest figuring out the chain of command.

IMO in a Nursing Home the person with the clout is the DON, in an AL it's the Administrator. If the move is very recent it could be that the staff on the floor haven't adjusted to his needs yet and things will improve in time.
(Of course the SW may be helpful as a liaison too, we don't usually have any here)

I would talk to the Director of the facility.